Optimal Loo(L2)-error estimates for the DG method applied to nonlinear convection-diffusion problems with nonlinear diffusion

• ID: 2481, RIV: 10057175
• ISSN: 0163-0563, ISBN: not specified
• source: Numerical Functional Analysis and Optimization
• keywords: optimal error estimates; discontinuous Galerkin; nonlinear convection-diffusion problems
• authors: Václav Kučera
• authors from KNM: Kučera Václav

Abstract

This article is concerned with the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonstationary convection-diffusion problem with nonlinear convection and nonlinear diffusion. Optimal estimates in the Loo(L2)-norm are derived for the symmetric interior penalty (SIPG) scheme in two dimensions. The error analysis is carried out for nonconforming triangular meshes under the assumption that the exact solution of the problem and the solution of a linearized elliptic dual problem are sufficiently regular.